Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(#10597243⋊C9) |
| unambiguous semidirect product | #10597243⋊(C22⋊C9) |
| unambiguous semidirect product | (C22⋊(C112⋊C9))⋊C5 |
| derived, Hall | C22×C112 ⋊ C5×C9 |
| Hall | C22⋊(C112⋊C9) ⋊ C5 |
| Hall | C22×#10597243 ⋊ C9 |
| Hall | #10597243 ⋊ C22⋊C9 |
| Sylow | C112 ⋊ C5×C22⋊C9 |
| Sylow | C22 ⋊ #10597243⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊((C112⋊C3)⋊C5) |
| commutator, hypocenter | C22×C112 | C5×C9 |
| Fitting, socle, cosocle | C22×C3×C112 | C3×C5 |
| prime radical | C22×C3×#10597243 | C3 |
| LCS | G ▷ C22×C112 | |
| UCS | C1 ◁ C3 | |
112 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,2^2,11^2,3|a^3=g,c^a=cd,d^a=c,e^a=e^2f^10,f^a=e^7f^8,e^b=e^4,f^b=f^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 213);